Notation

tation

Carl Friedrich Gauss alien the aboveboard bracket characters x for the attic action in his third affidavit of boxlike advantage (1808).2 This remained the standard3 in mathematics until Kenneth E. Iverson alien the names "floor" and "ceiling" and the agnate notations x and x in his 1962 book A Programming Language.45 Both notations are now acclimated in mathematics;6 this commodity follows Iverson.

The attic action is aswell alleged the greatest accumulation or entier (French for "integer") function, and its amount at x is alleged the basic allotment or accumulation allotment of x; for abrogating ethics of x the closing agreement are sometimes instead taken to be the amount of the beam function, i.e., the amount of x angled to an accumulation appear 0. The accent APL (programming language) uses ⌊x; added computer languages frequently use notations like entier(x) (Algol), INT(x) (BASIC), or floor(x)(C, C++, R, and Python).7 In mathematics, it can aswell be accounting with boldface or bifold brackets .8

The beam action is usually denoted by ceil(x) or ceiling(x) in non-APL computer languages that accept a characters for this function. The J Programming Language, a chase on to APL that is advised to use accepted keyboard symbols, uses >. for beam and <. for floor.9 In mathematics, there is addition characters with antipodal boldface or bifold brackets or just application accustomed antipodal brackets x.10

The apportioned allotment denticulate function, denoted by for absolute x, is authentic by the formula11

For all x,

editExamples

Sample amount x Floor Ceiling Fractional allotment

12/5 = 2.4 2 3 2/5 = 0.4

2.7 2 3 0.7

−2.7 −3 −2 0.3

−2 −2 −2 0